📐 Absolute Value Inequalities Calculator
Solve absolute value inequalities
|ax| < c
How to Use This Calculator
1
Choose Type
Select less than (<) or greater than (>)
2
Enter Values
Type coefficient a and constant c
3
Solve
See solution and interval notation
Rules
For |ax| < c:
Solve: -c < ax < c
Result: Interval between -c/a and c/a (not including endpoints)
For |ax| > c:
Solve: ax < -c OR ax > c
Result: Values less than -c/a or greater than c/a
About Absolute Value Inequalities Calculator
The Absolute Value Inequalities Calculator solves inequalities involving absolute values. For |ax| < c, find values between -c/a and c/a. For |ax| > c, find values outside this interval.
Key Concepts
- Less Than: Represents a bounded interval
- Greater Than: Represents a union of two unbounded intervals
- Two Cases: Always consider positive and negative possibilities
Remember
- |ax| < c has no solution if c < 0
- |ax| > c has all real numbers as solution if c < 0
- |ax| < 0 has no solution
Frequently Asked Questions
What's the difference between |x| < 3 and |x| > 3?
|x| < 3 means x is between -3 and 3. |x| > 3 means x is less than -3 or greater than 3.
How do I graph absolute value inequalities?
For <, shade between the two boundary values. For >, shade outside the boundary values.